%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : ITP072^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n010.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 04:01:53 EDT 2023

% Result   : Theorem 0.18s 0.52s
% Output   : Proof 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   50
% Syntax   : Number of formulae    :   58 (  17 unt;   6 typ;   1 def)
%            Number of atoms       :  125 (  23 equ;   0 cnn)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :  116 (  30   ~;  23   |;   0   &;  46   @)
%                                         (  16 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   24 (  22 usr;  22 con; 0-2 aty)
%            Number of variables   :   20 (   9   ^;  11   !;   0   ?;  20   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_hF_Mirabelle_hf,type,
    hF_Mirabelle_hf: $tType ).

thf(ty_eigen__0,type,
    eigen__0: hF_Mirabelle_hf ).

thf(ty_eigen__8,type,
    eigen__8: hF_Mirabelle_hf ).

thf(ty_hF_Mirabelle_hmem,type,
    hF_Mirabelle_hmem: hF_Mirabelle_hf > hF_Mirabelle_hf > $o ).

thf(ty_z,type,
    z: hF_Mirabelle_hf ).

thf(ty_zero_z189798548lle_hf,type,
    zero_z189798548lle_hf: hF_Mirabelle_hf ).

thf(h0,assumption,
    ! [X1: hF_Mirabelle_hf > $o,X2: hF_Mirabelle_hf] :
      ( ( X1 @ X2 )
     => ( X1 @ ( eps__0 @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(eigendef_eigen__8,definition,
    ( eigen__8
    = ( eps__0
      @ ^ [X1: hF_Mirabelle_hf] :
          ( ( hF_Mirabelle_hmem @ X1 @ zero_z189798548lle_hf )
         != ( hF_Mirabelle_hmem @ X1 @ z ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__8])]) ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: hF_Mirabelle_hf] :
        ~ ( hF_Mirabelle_hmem @ X1 @ zero_z189798548lle_hf ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ( ^ [X1: hF_Mirabelle_hf] : ( zero_z189798548lle_hf = X1 ) )
      = ( ^ [X1: hF_Mirabelle_hf] :
          ! [X2: hF_Mirabelle_hf] :
            ( ( hF_Mirabelle_hmem @ X2 @ zero_z189798548lle_hf )
            = ( hF_Mirabelle_hmem @ X2 @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: hF_Mirabelle_hf] :
        ( ( hF_Mirabelle_hmem @ X1 @ zero_z189798548lle_hf )
        = ( hF_Mirabelle_hmem @ X1 @ z ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: hF_Mirabelle_hf] :
        ~ ( hF_Mirabelle_hmem @ X1 @ z ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( ( hF_Mirabelle_hmem @ eigen__8 @ zero_z189798548lle_hf )
      = ( hF_Mirabelle_hmem @ eigen__8 @ z ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ! [X1: hF_Mirabelle_hf] :
        ( ( zero_z189798548lle_hf = X1 )
        = ( ! [X2: hF_Mirabelle_hf] :
              ( ( hF_Mirabelle_hmem @ X2 @ zero_z189798548lle_hf )
              = ( hF_Mirabelle_hmem @ X2 @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( hF_Mirabelle_hmem @ eigen__0 @ zero_z189798548lle_hf ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( zero_z189798548lle_hf = z ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( sP8 = sP3 ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( hF_Mirabelle_hmem @ eigen__8 @ z ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( z = zero_z189798548lle_hf ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ( sP7
      = ( hF_Mirabelle_hmem @ eigen__0 @ z ) ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ( hF_Mirabelle_hmem @ eigen__0 @ z ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ( ( ^ [X1: hF_Mirabelle_hf,X2: hF_Mirabelle_hf] : ( X1 = X2 ) )
      = ( ^ [X1: hF_Mirabelle_hf,X2: hF_Mirabelle_hf] :
          ! [X3: hF_Mirabelle_hf] :
            ( ( hF_Mirabelle_hmem @ X3 @ X1 )
            = ( hF_Mirabelle_hmem @ X3 @ X2 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ( hF_Mirabelle_hmem @ eigen__8 @ zero_z189798548lle_hf ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ! [X1: hF_Mirabelle_hf] :
        ( ( ^ [X2: hF_Mirabelle_hf] : ( X1 = X2 ) )
        = ( ^ [X2: hF_Mirabelle_hf] :
            ! [X3: hF_Mirabelle_hf] :
              ( ( hF_Mirabelle_hmem @ X3 @ X1 )
              = ( hF_Mirabelle_hmem @ X3 @ X2 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(conj_0,conjecture,
    sP11 = sP4 ).

thf(h1,negated_conjecture,
    sP11 != sP4,
    inference(assume_negation,[status(cth)],[conj_0]) ).

thf(h2,assumption,
    sP11,
    introduced(assumption,[]) ).

thf(h3,assumption,
    sP4,
    introduced(assumption,[]) ).

thf(h4,assumption,
    ~ sP11,
    introduced(assumption,[]) ).

thf(h5,assumption,
    ~ sP4,
    introduced(assumption,[]) ).

thf(h6,assumption,
    sP13,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP12
    | sP7
    | ~ sP13 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP3
    | sP12 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP9
    | ~ sP8
    | sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP6
    | sP9 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP1
    | ~ sP7 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP2
    | sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP16
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP14
    | sP16 ),
    inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP11
    | sP8 ),
    inference(symeq,[status(thm)],]) ).

thf(fact_1_hemptyE,axiom,
    sP1 ).

thf(fact_0_hf__ext,axiom,
    sP14 ).

thf(10,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h6,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,h2,h6,fact_1_hemptyE,fact_0_hf__ext]) ).

thf(11,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__0)],[h3,10,h6]) ).

thf(12,plain,
    ( ~ sP1
    | ~ sP15 ),
    inference(all_rule,[status(thm)],]) ).

thf(13,plain,
    ( ~ sP4
    | ~ sP10 ),
    inference(all_rule,[status(thm)],]) ).

thf(14,plain,
    ( sP5
    | sP15
    | sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(15,plain,
    ( sP3
    | ~ sP5 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8]) ).

thf(16,plain,
    ( ~ sP9
    | sP8
    | ~ sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(17,plain,
    ( ~ sP6
    | sP9 ),
    inference(all_rule,[status(thm)],]) ).

thf(18,plain,
    ( ~ sP2
    | sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(19,plain,
    ( ~ sP16
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(20,plain,
    ( ~ sP14
    | sP16 ),
    inference(prop_rule,[status(thm)],]) ).

thf(21,plain,
    ( ~ sP8
    | sP11 ),
    inference(symeq,[status(thm)],]) ).

thf(22,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h4,h5,h1,h0])],[12,13,14,15,16,17,18,19,20,21,h4,h5,fact_1_hemptyE,fact_0_hf__ext]) ).

thf(23,plain,
    $false,
    inference(tab_be,[status(thm),assumptions([h1,h0]),tab_be(discharge,[h2,h3]),tab_be(discharge,[h4,h5])],[h1,11,22,h2,h3,h4,h5]) ).

thf(24,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[23,h0]) ).

thf(0,theorem,
    sP11 = sP4,
    inference(contra,[status(thm),contra(discharge,[h1])],[23,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ITP072^1 : TPTP v8.1.2. Released v7.5.0.
% 0.13/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33  % Computer : n010.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Sun Aug 27 15:58:04 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.18/0.52  % SZS status Theorem
% 0.18/0.52  % Mode: cade22sinegrackle2x6978
% 0.18/0.52  % Steps: 1818
% 0.18/0.52  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------